baiz for you. At four your little one is going to pick up on your emotions during this time... so it's probably better to tell Chloe what happened in an age appropriate way, than let her become confused about how the grown ups in her world are behaving (as you all grieve). At 4, too, they start to understand death and often start to have a lot of questions about it.
So I suggest you work out how much she needs to know, and how to tell it to her simply. Be prepared to repeat yourself as she'll probably bring it up quite often over the next few months... that's all healthy for her, it's good for littlies to talk it out.
One last suggestion - let others in her support circle (Dad, other relatives, close friends etc) know what you've told her so they can confidently support and affirm what you've already said if she brings it up with them.
I'm sorry you (and your daughter) have to deal with such a difficult part of life so early in her life The best thing you can do for her is lots of love, affirmation and an increased reserve of patience as she works through it all.
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